There are two answers to your question, because the cold part of Europe is a big place.
In most of northern Europe, there are way fewer car crashes than in the USA. Two reasons. First, the driving tests are much harder in much of Europe than they are in North America, and the penalties for traffic violations are much harsher. Second, northern European countries have much more experience with snowstorms than most of the USA. A snowfall that wouldn't even be noticed in the north would wreak absolute havoc in much of the USA, because they don't know how to drive on snow.
But in Russia, the answer is very different. Because that whole country is functionally retarded when it comes to driving.